# Musical Scales

<-----------Massaging Screechy’s tension away using Solfege-like hand gestures

Wife’s entire family are classical musicians. She, and her brothers and parents, have perfect pitch. So, to answer the question way up there, most things in the world make some sound, many are a definable note or notes. They used to play “car horn” when they were kids. You know, who gets to nail the note first. My father in law gave us an IMMENSE air conditioner. It was brand new, but the compressor vibrated at a pitch that drove him insane ( it was in his violin studio ). Interesting people…

Cartooniverse

Mmmmmmmmmmmmm.
Kodaly.
Mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm.

Then again, the Guidonian hand is pretty, um, complicated…
Perfect pitch? Eh, that would drive me nuts. A friend was telling me about how his professor would torment the people with perfect pitch in sightsinging class:
He (the professor) would play a pitch on the piano and say, “That’s G sharp.”
People with perfect pitch in the class would argue “No no no that’s a D.”
“For the purpose of this exercise, this note <repeats note> is a G sharp. Now transcribe this” and he would play the melody. All the people with perfect pitch would struggle to write “G sharp” when they knew it was really “D”, as well as transpose the rest of the pitches.

Cruel but fun pranks to play on the gifted.

In the Washington Post dated 12-08-99 there is an excellent article on the origin of the musical scale. It also gives a good explanation of the basics of music theory. I think you can view or download articles from the Post going back 2 years. See Washingtonpost.com. The article is in Section H, pages 1 and 4.

Hi! This is my first response to anything here, so please be kind…

OK, about scales. First of all, sound frequency is a continuum, and the pitches we pick out are discrete points in that continuum. How many tones there are in an octave will depend on how closely or widely spaced those pitches are. So when we talk about a pentatonic scale we mean one with five pitches to the octave. The sixth pitch would be an octave above the first one. To change a five-note scale to a seven-note one you have to divide the octave differently.

To hear the pentatonic scale, just play only the black keys on a piano. Several people have mentioned that Chinese music uses this scale, but it has also been used all over the world, even in Western music. Lots of hymns and folktunes are pentatonic: e.g. Amazing Grace.

There is real physics behind the choice of pitches for a scale, which is why the same scales show up in different cultures. Different pitches have different frequencies of sound (i.e. how fast or slowly whatever is producing the sound is vibrating), and these frequencies are related to one another. In the middle ages, Music was taught in the universities as a part of mathematics – it was the science of Ratio rather than what we would consider music class to be today.

In the middle ages in France they would demonstrate the ratios with strings (it still works, btw – I’ve tried it in class). Take a string and divide it in half (producing the ratio 2:1). Half the string will vibrate exactly twice as fast as the whole string, and produce a pitch exactly one octave above that of the whole string. You can generate all the pitches in the scale this way, dividing the string into three and then four parts:

3:2 = the interval of a fifth (e.g. C-G on a piano)
4:3 = the interval of a fourth (e.g. C-F or G-C etc)

Dividing the string into 9 parts, you can generate a single tone (e.g. from C to D on the piano), with the sound ratio of 9:8. The smaller the numbers in a ratio, the better the two pitches will sound to us (music rather than noise).

Using different pitches as the basis for generating new pitches, you can find all seven pitches of Western scales this way. The tradition is that the philosopher Pythagoras (6th century BC) discovered this method of determining the pitches of a scale – the kind of tuning this method produces is called “pythagorean” to this day. And this is why Western scales have seven pitches, with the 8th an octave above the first: we’ve been teaching ourselves to divide the octave this way for over two thousand years.

Someone has already mentioned the American composer Harry Partch. He was fascinated with the history of tuning and intonation. His book Genesis of a Music (1949, 2nd ed. Da Capo Press, 1974) has a chapter on the history of tuning systems that is the best and most consise discussion of this topic that I know.

One last thing: nobody asked it, but I can tell you where the “do re mi” syllables come from. Guido of Arezzo (an Italian musician/teacher who lived c.1000-1050) taught his students to sing a major scale using a gregorian chant hymn to St. John the Baptist called “Ut queant laxis”. Guido had noticed that each phrase of the hymn began on a different scale pitch, starting on C and moving up. He used the syllables that began each phrase as the name for that pitch:

UT queant laxix
REsonare fibris
MIra gestorum
FAmuli tuorum,
SOLve polluti
LAbii reatum, Sancte Joannes.

[“That thy servants may freely proclaim the wonders of thy deeds, absolve the sins of their unclean lips, O holy John”]

“Ut” (pronounced Oot) was changed to “Do” (pronounced Doh) in the 20th century. But I have no idea who did it, or why.

OK. All the modes had names in the Greek system. They were actually described in Plato’s Republic, book 3, one of the earliest such catalogues to have survived. Here’s the complete list:

Scales played by striking the white keys starting with

C (the major scale): Ionian.
D: Dorian. (the scale Plato eventually favours.)
E: Phrygian.
F (the minor scale): Lydian.
G: Mixolydian.
A: Aeolian (possibly what Plato refers to as “Syntonolydian”).

And they are not named after bodily humours, but after regions of the Greek empire.

This is the scale used on the bagpipes, with repetition, to nine notes in total. That’s why most Scots music from the pipes can be played only on the black keys.

From what I’ve read, the pentatonic scale is so common in folk music because there is not much scope for variation in a simple pipe instrument. Most primitive pipes are about the same size and have the finger holes spaced about the same distance apart. (For example, I was playing my chanter for my brother-in-law the other night, and he said it sounded like a snake charmer’s pipe.)

The confusing thing about reading pipe music is that by convention, the notes are written down by the usual Western European notation, rather than writing out the notes of the actual pentatonic scale, given above. Playing from G to G[sup]1[/sup] on the chanter sounds nothing like the scale of G major on the piano - the intervals are wrong.

Thank you for the clarification, matt_mcl. I knew they were named after different regions and influenced the bodily humors, but was twiching too much at that point to correct it in the re-reading.

jti - My sourcebook indicated Scottish music (as well at least a dozen others), but wasn’t quite sure which aspect. Pipes, duh!

:sound of one hand slapping one head:

On a guitar you can divide the string as Speranza described by touching (but not fretting) the string at certain points, they are called ‘touch harmonics’. If you touch at the 12th fret (exactly between the nut and the bridge) and pick it, the string will vibrate twice as fast as if you play it open, if you look at it under the right light you will see that it is two waves, the string barely moving in the middle. If you touch at the 7th fret, it will divide into three waves, and it will play a note an octave and a fifth above the open note. If you touch it at the 5th fret (which is exactly halfway between the nut and the twelth fret), it will play a note two octaves higher…the fourth fret is (I believe) two octaves and a fifth…or is it a third… Higher up, the touch points don’t correspond with the frets exactly, the next big one is about 3/4 of the way from the second to the third fret, the one that will get you three octaves higher is one fifth of the way from the second to the third. You can barely hear those last two because the string is divided up into so many waves that it’s not moving very far on each one, but on an electric with compression and maybe some distortion you can hear it. You can play the first few notes of the Star Trek theme using only touch harmonics on the A and E strings, and you can play Taps with touch harmonics on just one string. The sound effect the transporters used in some of the Star Trek movies (2 and 3 I think) incorporated the sound you get if you rapidly pick the string while sliding your finger along the string, getting all the touch harmonics along the way. A lot of modern electric guitar music also uses what’s called ‘pinch harmonics’. This is where you extend the end of your thumb a bit past the pick and touch the string as you pick it, if you do it in the right place the guitar will squeal several octaves above the note you fretted (because your hand is so close to the bridge). ZZ Top, Pantera, and Randy Rhodes-era Ozzy used it a lot. When you hear a guitar playing fairly low notes and suddenly it squeals much higher than the note before, it’s probably pinch harmonics. Before I learned that, figuring out how the pitch could jump so high so suddenly drove me nuts.

The violin has the touch harmonic phenomenon as well. I can only do it with the octave, but if I noodle around some more I should be able to get the same effects.

As for the Greek scales, the previous posters have forgotten the Locrian scale, and example of which would be playing the C major scale starting from B.

screech-owl: Those notebooks could be a very valuable commodity. They should be protected from self-teaching theory students who might want an unethical leg up via someone else’s hard-won studies. evil grin

This is because those harmonics don’t apply only to strings. All brass instruments use harmonics to produce their range of notes (ever notice there’s only three (or four) keys? That’s only eight different notes.)

In the case of Taps, specifically, a bugle, which has no keys, uses harmonics to create all of its sounds. The harmonics are formed on the column of air, rather than a string. If you look, you’ll find all bugle music is written with four or five notes, total, all simple harmonics.

(I’m a violinist, and I hate when the parts call for harmonics. I personally think they don’t sound very good. OTOH, a similar concept is useful for producing vibrato while playing an open string).

LL

LOCRIAN!!!
Dammit, that’s it!
Kept me awake half the night trying to remember my modes! Although one of my theory teachers gave us the impression that Locrian was a synthetic mode, ‘made up so [b-b[sup]1[/sup]] wouldn’t be lonely’, and was not an actual mode in use with the Greeks. Can anyone verify or refute that?
White key scales

Ionian - c-c[sup]1[/sup]
Dorian - d-d[sup]1[/sup]
Phrygian - e-e[sup]1[/sup]
Lydian - f-f[sup]1[/sup]
Myxolydian - g-g[sup]1[/sup]
Aeolian - a-a[sup]1[/sup]
Locrian - b-b[sup]1[/sup]

[singing]
And that brings us back to IO[sub]nian[/sub].
[/singing]

If
Doris
Plays
Lydian,
Matt
Locrian.

And Olentzero, I’d be happy to share my notebooks (and subsequent knowledge) with you. Can’t guarantee everything is correct or legible, but ask away.

[QUOTE]
*Originally posted by screech-owl *
**LOCRIAN!!!
Dammit, that’s it!
Kept me awake half the night trying to remember my modes! Although one of my theory teachers gave us the impression that Locrian was a synthetic mode, ‘made up so [b-b[sup]1[/sup]] wouldn’t be lonely’, and was not an actual mode in use with the Greeks. Can anyone verify or refute that?

Actually, what WE call Locrian probably was used by the Greeks, only they called it Mixolydian!

It’s a common misconception that the modes used by Medieval theorists were the same as those referred to by the Greeks. In fact, when “our” modal system was developed around the 10th century CE, the monks got all the names mixed up. Just a sample of final ("tonics), our name, Greek name:

B - Greeks - Mixolydian; Us - Locrian
C - Greeks - Lydian; Us - Ionian
D - Greeks - Phrygian; Us - Dorian
E - Greeks - Dorian; Us - Phrygian

You are right, though, that when the modal system was re-invented by Western European musicians, (what we call) the Locrian mode was thrown in just so we’d have a mode built on B.

I’m pleasantly surprised that a thread on modal theory is getting so much interest! Medievalists of the world unite!

D18

Pardon the newby screwing up the bolding. Just to get the typography right, that should be:

Actually, what WE call Locrian probably was used by the Greeks, only they called it Mixolydian!

It’s a common misconception that the modes used by Medieval theorists were the same as those referred to by the Greeks. In fact, when “our” modal system was developed around the 10th century CE, the monks got all the names mixed up. Just a sample of final ("tonics), our name, Greek name:

B - Greeks - Mixolydian; Us - Locrian
C - Greeks - Lydian; Us - Ionian
D - Greeks - Phrygian; Us - Dorian
E - Greeks - Dorian; Us - Phrygian

You are right, though, that when the modal system was re-invented by Western European musicians, (what we call) the Locrian mode was thrown in just so we’d have a mode built on B.

I’m pleasantly surprised that a thread on modal theory is getting so much interest! Medievalists of the world unite!

D18

I love thinking about modes in music, and as a guitarist, it was an epiphany when I happened upon this concept and how it relates to what chords are chosen in a song, as well as what notes to choose when soloing. Thinking modally allows you to abandon the concept of “key”, making each key equally understandable as another. Wanna play in in G# minor instead of Bb minor? No problem!

C (the major scale): Ionian.

Much music is in this mode. It is the happy mode.

D: Dorian. (the scale Plato eventually favours.)

This is the Allman Brothers/Santana mode. With the sixth not flatted, it is a sad, but not as sad the aeolian. Think “Whipping Post”, or maybe “So What” by Miles Davis.

E: Phrygian.

Similar to Locrian. Odd and Eastern or maybe spanish sounding. Think “White Rabbit” by Jefferson Airplane or maybe “Syeeda’s Song Flute” by Coltrane, or maybe flamenco music.

F (the is NOT the minor scale): Lydian.
Not heard too much except perhaps in jazz or modern art music.
**G: Mixolydian: **

Contemplative and moody with it’s flatted 7th note, but with a major 3rd, not as sad. This is the Grateful Dead key, also heard a lot in rock & jazz.

**A: Aeolian: **

Actually THIS is the minor scale. The sad one. Think Niel Young or Pink Floyd. Think funeral dirge.

**B: Locrian. **

Also odd-ball sounding, but not as minor as Phrygian. Maybe think klezmer.

Also a not on the pentatonic blues [minor] scale: Originally, the notes were 1st, halfway between minor third and third, fourth, halfway between flatted fifth and fifth, and halfway between dominant and major 7th. Those halfway notes are sometimes referred to as “blue” notes. When you can play these notes, like with voice, guitar or sax, it can really sound bluesy. Obviously, these “halfway” notes cannot be produced accurately on the piano, so some folks just mash both keys to simulate those blue notes.

The pentatonic scale, both minor[blues& rock] and major[country & rock], is the salvation of the amatuer guitar soloist as well as Frank Zappa.

I do it 8 days a week.

Wait, that’s a regular minor, isn’t it? (There’s probably a better adjective than “regular”.) I thought the harmonic minor was:

c – d – e-flat – f – g – a-flat – b – c[sup]1[/sup]

If that’s not a harmonic minor, I’m going to claim it as Greg’s minor, because I’ve always liked it.

Dammit, now I’m all confused.
And I thought I had a headache last night while deciphering my notes from college [sub]mumblednumber[/sub] years ago.
Let me look that up and get back to you, unless someone wants to correct me on this first.

(What’s my batting average about now? .00007? Well, at least I am keeping you all on your toes and I know someone is actually reading my posts - 'cause from the looks of it, it sure ain’t me!)

There’s harmonic minor, melodic minor (differs ascending and descending) and ‘pure’ minor (if I took notes correctly). I’m stopping at the library after work anyway: I’ll look this up.

<SNIP>

Greg is right on this one, screech. There’s a bazillian more minor scales, too, based on the modes from the harmonic and melodic minors. Here are a fe oddballs:

Locrian natural 6th (1 2 b3 #4 5 b6 b7 8)
Dorian augmented 4th (1 2 b3 #4 5 b6 b7 8)
Altered Dominant bb7 (1 b2 b3 b4 b5 b6 bb7 8)

Just don’t make me solo in them.

There are three forms of the minor key in Western music theory. They are the melodic, the harmonic, and the natural.

The melodic has only one flat in the octave, namely a minor 3rd:

C D Eb F G A B C

The harmonic has two flats, namely a minor third and a minor 6th:

C D Eb F G Ab B C

The natural has three flats, namely a minor third, a minor sixth, and a minor seventh:

C D Eb F G Ab Bb C

The only application I’m aware of (since I haven’t studied but a small amount of theory) is in the construction of four-part chords when using the minor keys.

Just to further confuse the issue, this is true only of the ascending form. Descending it’s C B-flat A-flat G F E-flat D C.

It has to do with the development of keys from modes. Originally you had the Aeolian mode:

A B C D E F G A

But in actual practice, the F and the G tended to be raised in ascending passages of music, and lowered back down on descending passages. Thus, the minor scale.

That’s actually how the major scale came to be too. On the one hand you had the Mixolydian mode:

G A B C D E F G

But in actual practice, the F tended to be raised to F-sharp most of the time. Similarly you had the Lydian mode:

F G A B C D E F

But the tritone between the F and the B sounded “evil” - and was called “the devil in music” - so in actual fact the B tended to be lowered to a B-flat in actual music.

Yes, there is an Ionian mode:

C D E F G A B C

But it was not set down in theory books until about the 16th century, IIRC. At any rate, not till long after the original four modes. About the same time, the Aeolian mode was codified as well.

Modes and keys were codified well after the fact - as a way of explaining musical intuitions, so a lot of theory has to be massaged to fit the musical practice.

D18